Cho hệ phương trình

- Hướng dẫn giải

Đáp án: D

Khi đó

$$\begin{gathered} \left\{\begin{array}{l}\left(m^2-m-2\right)y=2m^2+3m-5\\ x=2m+3-my\end{array}\right. \\ \iff \left\{\begin{array}{l}y=\frac{2m^2+3m-5}{m^2-m-2}\\ x=2m+3-my\end{array}\right. \end{gathered}$$

Để phương trình có nghiệm y<0 thì: $\frac{2m^2+3m-5}{m^2-m-2}<0$

$\iff \left[\begin{array}{c}\left\{\begin{array}{l}2m^2+3m-5<0\\ m^2-m-2>0\end{array}\right.\\ \left\{\begin{array}{l}2m^2+3m-5>0\\ m^2-m-2<0\end{array}\right.\end{array}\right.\iff \left[\begin{array}{c}\left\{\begin{array}{l}\frac{-5}{2}<m<1\\ m<-1 hoặc m>2\end{array}\right.\\ \left\{\begin{array}{l}m<\frac{-5}{2} hoặc m>1\\ -1<m<2\end{array}\right.\end{array}\right.\iff \left[\begin{array}{c}\frac{-5}{2}<m<-1\\ 1<m<2\end{array}\right.$